Conditional Stability Estimates for Ill-Posed PDE Problems by Using Interpolation

Autor:	Uno Hämarik, Bernd Hofmann, U. Tautenhahn, Y. Shao
Přispěvatelé:	Hochschule Zittau/Görlitz, Universität Tartu - Estonia
Rok vydání:	2013
Předmět:	Well-posed problem Mathematical optimization Inkorrekt gestellte Probleme Control and Optimization Partial differential equation Inverse quadratic interpolation Ill-posed problems inverse problems conditional stability estimates interpolation elliptic problems parabolic problems source problems analytic continuation Analytic continuation MathematicsofComputing_NUMERICALANALYSIS Inverse Inverse problem Computer Science Applications Inverses Problem Inkorrekt gestelltes Problem Lineare partielle Differentialgleichung Signal Processing ddc:515 Analysis Variable (mathematics) Mathematics Interpolation
Zdroj:	Numerical Functional Analysis and Optimization. 34:1370-1417
ISSN:	1532-2467 0163-0563
Popis:	The focus of this paper is on conditional stability estimates for ill-posed inverse problems in partial differential equations. Conditional stability estimates have been obtained in the literature by a couple different methods. In this paper we propose a method called interpolation method, which is based on interpolation in variable Hilbert scales. We are going to work out the theoretical background of this method and show that optimal conditional stability estimates are obtained. The capability of our method is illustrated by a comprehensive collection of different inverse and ill-posed PDE problems containing elliptic and parabolic problems, one source problem and the problem of analytic continuation.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1932737e9f608695256538bd9cc7424b https://doi.org/10.1080/01630563.2013.819515 Zobrazit plný text záznamu Plný text ve formátu PDF Plný text ve formátu HTML
Nepřihlášeným uživatelům se plný text nezobrazuje	K zobrazení výsledku je třeba se přihlásit.